There's no definite answers on this point yet, as far as I know.
If you assume that they are their realms: I suppose that then Daedric princes cannot destroy intruders any more than you can consciously destroy germs that enter your body. At least in the case of princes that don't directly invite you into their realm, the Daedric planes tend to be hazardous while not insurmountable.
But then you could equally consider this evidence that the Daedra are distinct from their planes. They are said to have created their realms from stolen creatia (magical/mythical energy), so I suppose that that's evidence that the "prince" and the realm are different things. Also:
(http://www.imperial-library.info/content/mythic-dawn-commentaries-vol-4)
(http://www.imperial-library.info/content/fight-three-snow-whale-and-dirtbird)
Both these quotes imply that the ruler of a Daedric realm can change, so the Prince and the plane are separable.